#### Answer

$\color{blue}{\left\{-416, 16\right\}}$

#### Work Step by Step

The numerator of the rational exponent is even so raising both sides to $\frac{5}{2}$ will not work.
Raise both sides to the 3rd power to obtain:
$((x+200)^{2/3})^3=36^3
\\(x+200)^2=46,656$
Take the square root of both sides to obtain:
$\sqrt{(x+200)^2}=\pm \sqrt{46,656}
\\x+200 = \pm \sqrt{216^2}
\\x+200 = \pm 216$
Add $-200$ to both sides of the equation to obtain:
$\\x=-200 \pm 216
\\x_1=-200-216=-416
\\x_2=-200+216=16$
Upon checking both proposed solutions satisfy the original equation.
Thus, the solutions set is $\color{blue}{\left\{-416, 16\right\}}$.